Question

if the height of a right circular cone is 24cm and surface area is 550 square cm. find its volume.

Answer 1

Given

(Curved Surface area of a Cone = pi r L, where r is the radius of the base & L is its slant height.

Height(h) of the cone = 24cm.

So, in right triangle slant height L= √( h² + r²) = √(24² + r²)

= √(576+r²)

Pi r L = 550

=> pi * r * (√(24² + r²) = 550

=> pi² * r² * ( 24² + r²) = 550² ( On squaring)

=> 576pi²r² + pi²r^4 = 550²

=> pi² r^4 + 576pi² r² - 550² =0

Let r² be x

=> pi²x² + 576pi²x - 550² =0

=> 22/7 *22/7 *x² + 576*22/7*22/7 -2²*5²*5²*11²= 0 Now divide each term by 11²

=> 4/49x² + 576*4/49 *x - 2500=0

= 4x² + 2304x - 122500 =0 ( by multiplying each term by 49)

=> x² + 576x - 30625 = 0

=> x = (-576 +,-√454276)/2

x = (-576 + 674)/2 ( -ve value is ruled out)

=> x = 98/2 = 49

=> r² = 49

=> r = 7

So, Volume of Cone = 1/3* pi* r² * h

=> Volm = 1/3 * 22/7 * 7*7*24

= Volm = 22*7*8

=> 1232 cu cm ………ANS.

Answer 2

I hope it will help u.